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# the last digit of 3^3^3

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the last digit of 3^3^3 [#permalink]  18 Aug 2009, 08:00
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0% (00:00) correct 100% (00:25) wrong based on 1 sessions
I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?
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Re: the last digit of 3^3^3 [#permalink]  18 Aug 2009, 09:26
flyingbunny wrote:
I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?

well that reduces into 3^27 right? now you should know the pattern of 3^p is:
1,3,9,7,1,3 etc. starting from p=0. so 28/4 7. So you get to 7. 28 is 27 (1-27) + 1(0th power). It is also simple to count if you really wanted.
Just to clarify - since the pattern for 3^p happens every 4 powers when you divide the power by 4 the remainder determines the position of the digit. In this example .25 = 1, .5=3,.75=9, 1 (or nor remainder) = 7.
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Last edited by shaselai on 18 Aug 2009, 09:30, edited 1 time in total.
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Re: the last digit of 3^3^3 [#permalink]  18 Aug 2009, 09:29
flyingbunny wrote:
I took the free test of GMAT club. One of the questions is as below.

I choose that "the last digit is 3", but the answer key says "the last digit is 7". The answer key is incorrect, isn't it?

You find some good discussions and concepts.
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Re: the last digit of 3^3^3 [#permalink]  18 Aug 2009, 10:30
http://en.wikipedia.org/wiki/Exponentiation

according to this, the answer of "the last digit of 3^3^3" should be 7.

if you know the sequence of computing exponentiation, this question is a piece of cake, otherwise you would never get the answer right.
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Re: the last digit of 3^3^3   [#permalink] 18 Aug 2009, 10:30
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